The Annals of Probability

The Minimal Eigenfunctions Characterize the Ornstein-Uhlenbeck Process

J. C. Taylor

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Abstract

A process $(X_t)$ is equivalent to an Ornstein-Uhlenbeck process if and only if $e^{-\lambda t}f(X_t)$ is a martingale for every $f \geq 0$ on $\mathbb{R}^d$ such that $\Delta f(x) - \langle x, \nabla f(x)\rangle = \lambda f(x)$.

Article information

Source
Ann. Probab., Volume 17, Number 3 (1989), 1055-1062.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991256

Digital Object Identifier
doi:10.1214/aop/1176991256

Mathematical Reviews number (MathSciNet)
MR1009444

Zentralblatt MATH identifier
0686.60084

JSTOR
links.jstor.org

Subjects
Primary: 60J60: Diffusion processes [See also 58J65]
Secondary: 60G44: Martingales with continuous parameter

Keywords
Eigenfunctions Ornstein-Uhlenbeck process characterization martingales

Citation

Taylor, J. C. The Minimal Eigenfunctions Characterize the Ornstein-Uhlenbeck Process. Ann. Probab. 17 (1989), no. 3, 1055--1062. doi:10.1214/aop/1176991256. https://projecteuclid.org/euclid.aop/1176991256


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